Standardized TestingStandardized TestingStandardized TestingStandardized Testing

Basic Terminology

•Evaluation: a judgment•Measurement: a number•Assessment: procedure to

gather information

Norm- and Criterion-Referenced Tests

• Norm-referenced– General ability– Compares

people to people

– Selecting top candidates

• Criterion-referenced– Mastery– Basic skills– Prerequisites– Grouping for

instruction

What Do Test Scores Mean?

• Standardized test • Norming sample• Frequency distributions• Central tendency• Variability

Frequency Distribution Histogram

0

0.5

1

1.5

2

2.5

3

Students

40 45 50 55 60 65 70 75 80 85 90 95 100

Scores on Test

Central Tendency• Mean

– The arithmetic average • Median

– The middle score• Mode

– The most frequently occurring score

Variability• Range• Standard deviation

– Indicates how much the scores vary from the mean

Calculating the Standard Deviation

• Calculate the mean: • Subtract the mean from each score: • Square each difference:

• Add all the squared differences:

• Divide by the number of scores:

• N• Find the square root : N

Sample Problems

Calculate the mean, median, mode, range, and standard

deviation for the following sets of scores

• Reading– 95– 90– 85– 80– 75– 70– 65– 60– 55

• Arithmetic– 76– 78– 77– 71– 75– 79– 74– 72– 73

Calculations• Reading

– 95 20 400– 90 15 225– 85 10 100– 80 5 25– 75 0 0– 70 -5 25– 65 -10 100– 60 -15 225– 55 -20 400

• Arithmetic

– 76 +1 1– 78 +3 9– 77 +2 4– 71 -4 16– 75 0 0– 79 +4 16 – 72 -3 9– 73 -2 4– 74 -1 1

=12.91

Calculations continuedReading

Arithmetic

Standard deviations

Completed CalculationsReading

– Mean = 75– Mode = none– Median = 75– Range = 40– Standard

deviation = 12.91

Arithmetic– Mean = 75– Mode = none– Median = 75– Range = 8– Standard

deviation = 2.58

Normal Distributions• The “bell curve”• Mean, median, mode all at the

center of the curve• 50% of scores above the mean• 50% of scores below the mean

Normal Distribution with Standard Deviations

2%2% 2%2%34%34%

14% 14%

0 +1SD-1SD-2SD +2SD-3SD +3SD

Percent of the population

Standard Deviation Units

Types of Scores

• Percentile rank• Grade-equivalent• Standard scores

– z scores– T scores– Stanine scores

Interpreting Test Scores

• Reliability• True score• Standard error• Confidence

intervals • Validity

Types of Standardized Tests

• Achievement Tests – Measure previous learning

• Diagnostic Tests– Identify strengths and weaknesses

• Aptitude Tests– Measure abilities

Issues in Testing

•Widespread testing

•Accountability and high stakes testing